Use Of Gradient Decent Function In Cryptography

ABSTRACT

A method of encrypting and decrypting multiple individual pieces or sets of data in which a computing device randomly selects a group of seeds that it then uses to generate irrational numbers. Sections of the generated irrational numbers can be used as one-time pads or keys to encrypt the corresponding data sets. Intended recipients can then reverse the process using their allowed keys to access data for which they have authorization.

FIELD OF THE INVENTION

The field of the invention is data security.

BACKGROUND

The background description includes information that may be useful inunderstanding the present invention. It is not an admission that any ofthe information provided herein is prior art or relevant to thepresently claimed invention, or that any publication specifically orimplicitly referenced is prior art.

Encryption relying on prime numbers or quasi-prime numbers, such aspublic-private key cryptography schemes (e.g., the RSA encryptionscheme), has historically been extremely secure due to thecomputationally-intensive efforts needed to crack large public keys.

However, as computational resources evolve and new areas emerge (such asquantum computing), the security of these schemes will become weaker andweaker as prime numbers become easier to solve.

One-time pads for passwords are known to be completely secure. However,the use of one-time pads requires that the keys be shared between theparties ahead of time and only be used once. This means that for manyexchanges, the parties must have a priori storage of many keys. Thedifficulties associated with these requirements has resulted in favoringthe public key cryptography schemes over one-time pad schemes.

One-time pads for passwords are known to be have a high level ofsecurity. However, the use of one-time pads requires that the keys beshared between the parties ahead of time, and only be used once. Thismeans that for many exchanges, the parties must have a priori storage ofmany keys. The difficulties associated with these requirements hasresulted in favoring the public key cryptography schemes over one-timepad schemes.

My co-pending application Ser. No. 17/018,582 “Methods of Storing andDistributing Large Keys”, discloses methods of using sequences withinirrational or transcendental numbers as one-time key pads, and storinginformation for deriving such sequences instead of the entire sequences.

Others have attempted to solve this problem. WO 20190110955 to Bryantdiscusses the use of a one-time pad for password generation. However,the solution in Bryant requires the storage of all of the passwords in alarge pad, which is resource intensive. WO 00/65768 to Persson discussesdetermining a maximum key length. However, the generation of theshortened key in Persson is performed in such a way that a function canstill only be used once.

Thus, there is still a need for a system that securely protects a shareddata set while adeptly providing the correct access to its users.

SUMMARY OF THE INVENTION

The inventive subject matter provides apparatus, systems and methods inwhich a computing device produces highly random numbers using acombination of (1) and AI interface, (2) a functions table, and (3) arandom bits generator.

In embodiments, the inventive subject matter provides apparatus, systemsand methods in which a computing device obtains a random selection ofseeds, then proceeds to apply one or more functions against the selectedseeds to produce corresponding irrational numbers. The computing deviceuses portions of the irrational numbers as one-time pads to encryptcorresponding individual pieces of data/data sets. For additionalsecurity, the computing device then avoids reusing the selected seeds.In embodiments, the computing device can delete the previously usedseeds.

In embodiments, the seeds in the randomly-selected group are neitherprime numbers nor quasi-prime numbers.

In embodiments, the computing device randomly selects seeds from a poolof seeds that was previously used to select random groups of seeds forprior operations.

To decrypt, a decrypting computing device obtains at least one seed andan indication of a function, and a start location and length, so as togenerate a decryption one-time pad.

Various objects, features, aspects and advantages of the inventivesubject matter will become more apparent from the following detaileddescription of preferred embodiments, along with the accompanyingdrawing figures in which like numerals represent like components.

All publications identified herein are incorporated by reference to thesame extent as if each individual publication or patent application werespecifically and individually indicated to be incorporated by reference.Where a definition or use of a term in an incorporated reference isinconsistent or contrary to the definition of that term provided herein,the definition of that term provided herein applies and the definitionof that term in the reference does not apply.

The following description includes information that may be useful inunderstanding the present invention. It is not an admission that any ofthe information provided herein is prior art or relevant to thepresently claimed invention, or that any publication specifically orimplicitly referenced is prior art.

In some embodiments, the numbers expressing quantities of ingredients,properties such as concentration, reaction conditions, and so forth,used to describe and claim certain embodiments of the invention are tobe understood as being modified in some instances by the term “about.”Accordingly, in some embodiments, the numerical parameters set forth inthe written description and attached claims are approximations that canvary depending upon the desired properties sought to be obtained by aparticular embodiment. In some embodiments, the numerical parametersshould be construed in light of the number of reported significantdigits and by applying ordinary rounding techniques. Notwithstandingthat the numerical ranges and parameters setting forth the broad scopeof some embodiments of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspracticable. The numerical values presented in some embodiments of theinvention may contain certain errors necessarily resulting from thestandard deviation found in their respective testing measurements.

Unless the context dictates the contrary, all ranges set forth hereinshould be interpreted as being inclusive of their endpoints andopen-ended ranges should be interpreted to include only commerciallypractical values. Similarly, all lists of values should be considered asinclusive of intermediate values unless the context indicates thecontrary.

As used in the description herein and throughout the claims that follow,the meaning of “a,” “an,” and “the” includes plural reference unless thecontext clearly dictates otherwise. Also, as used in the descriptionherein, the meaning of “in” includes “in” and “on” unless the contextclearly dictates otherwise.

The recitation of ranges of values herein is merely intended to serve asa shorthand method of referring individually to each separate valuefalling within the range. Unless otherwise indicated herein, eachindividual value is incorporated into the specification as if it wereindividually recited herein. All methods described herein can beperformed in any suitable order unless otherwise indicated herein orotherwise clearly contradicted by context. The use of any and allexamples, or exemplary language (e.g. “such as”) provided with respectto certain embodiments herein is intended merely to better illuminatethe invention and does not pose a limitation on the scope of theinvention otherwise claimed. No language in the specification should beconstrued as indicating any non-claimed element essential to thepractice of the invention.

Groupings of alternative elements or embodiments of the inventiondisclosed herein are not to be construed as limitations. Each groupmember can be referred to and claimed individually or in any combinationwith other members of the group or other elements found herein. One ormore members of a group can be included in, or deleted from, a group forreasons of convenience and/or patentability. When any such inclusion ordeletion occurs, the specification is herein deemed to contain the groupas modified thus fulfilling the written description of all Markushgroups used in the appended claims.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a diagrammatic overview of a system according to variousembodiments of the inventive subject matter.

FIG. 2 provides a schematic representation of the AI general workflow,according to embodiments of the inventive subject matter.

FIG. 3 provides a schematic representation of a small part of theFunctions Table, according to embodiments of the inventive subjectmatter.

FIG. 4 provides a schematic representation of the RBG workflow,according to embodiments of the inventive subject matter.

FIG. 5 shows a flowchart of a method of securing data, according toembodiments of the inventive subject matter.

FIG. 6 illustrates the processes associated with encrypting a set ofdata according to embodiments of the inventive subject matter.

DETAILED DESCRIPTION

Throughout the following discussion, numerous references will be maderegarding servers, services, interfaces, engines, modules, clients,peers, portals, platforms, or other systems formed from computingdevices. It should be appreciated that the use of such terms, is deemedto represent one or more computing devices having at least one processor(e.g., ASIC, FPGA, DSP, x86, ARM, ColdFire, GPU, multi-core processors,etc.) programmed to execute software instructions stored on a computerreadable tangible, non-transitory medium (e.g., hard drive, solid statedrive, RAM, flash, ROM, etc.). For example, a server can include one ormore computers operating as a web server, database server, or other typeof computer server in a manner to fulfill described roles,responsibilities, or functions. One should further appreciate thedisclosed computer-based algorithms, processes, methods, or other typesof instruction sets can be embodied as a computer program productcomprising a non-transitory, tangible computer readable media storingthe instructions that cause a processor to execute the disclosed steps.The various servers, systems, databases, or interfaces can exchange datausing standardized protocols or algorithms, possibly based on HTTP,HTTPS, AES, public-private key exchanges, web service APIs, knownfinancial transaction protocols, or other electronic informationexchanging methods. Data exchanges can be conducted over apacket-switched network, the Internet, LAN, WAN, VPN, or other type ofpacket switched network.

The following discussion provides many example embodiments of theinventive subject matter. Although each embodiment represents a singlecombination of inventive elements, the inventive subject matter isconsidered to include all possible combinations of the disclosedelements. Thus if one embodiment comprises elements A, B, and C, and asecond embodiment comprises elements B and D, then the inventive subjectmatter is also considered to include other remaining combinations of A,B, C, or D, even if not explicitly disclosed.

As used herein, and unless the context dictates otherwise, the term“coupled to” is intended to include both direct coupling (in which twoelements that are coupled to each other contact each other) and indirectcoupling (in which at least one additional element is located betweenthe two elements). Therefore, the terms “coupled to” and “coupled with”are used synonymously.

FIG. 1 provides a diagrammatic overview of a system 100 according toembodiments of the inventive subject matter.

The inventive subject matter provides apparatus, systems and methods inwhich a computing device produces highly random numbers using acombination of (1) and AI interface, (2) a functions table, and (3) arandom bits generator.

A preferred embodiment of the inventive system and method is referred toherein from time to time as CrownRNG™. The CrownRNG™ design exploits theby-default randomness of irrational numbers.

Mathematically speaking, irrational numbers are those numbers thatcannot be expressed as ratios of two or more rational numbers. They areproven to have digital sequences, also known as mantissas, that extendto infinity without ever repeating. Therefore, they are excellentsources for true randomness1.

Mathematical functions known to generate irrational numbers include thesquare roots of non-square numbers, e.g., square roots of prime numbers,?20, ?35, etc., and also trigonometric functions having natural numbersfor their arguments, among many other. (Please refer to Appendix A for alist of some irrational numbers' generating functions).

The basic idea behind CrownRNG is to use the power of artificialintelligence (AI) to create mathematical functions able to generaterandom irrational numbers. The irrational numbers will function asparameters to be used to generate highly randomized sequences of binarybits that are suitable for encryption purposes.

The CrownRNG unit generally comprises three main components:

-   -   1—An AI interface.    -   2. A Functions Table.    -   3. A Random Bits Generator (RBG).

1. The AI interface:

The AI interface utilizes the learning capabilities of artificialintelligence to learn how to generate randomized parameters needed bythe system.

The AI is initialized by a set of CPU metrics coming from the hostingPC. It uses these metrics as initial features to learn from and to thenevolve via linear-regression-based Machine-Learning (ML) algorithm.

One branch of the AI, the MusicAI, will compose random music pieces thatwill transform into a set of numbers corresponding to the octaves,notes, and tempi of the music piece. These three values are thenconverted, via digital root arithmetic, into specific ranges such thatthey can be utilized by the Functions Table.

The other branch of the AI, the MathAI, uses ML to create ever-changingmathematical formulae tuned to create random non-square numbers (N). Thesquare roots of these non-square numbers create numbers with irrationalmantissas. These irrational numbers will be truncated to specificbit-lengths dictated by the private keys' security level and then willbe passed on to the RBG as seeds.

The MusicAI:

The main workflow of the MusicAI can be summarized as follows:

First, three parameters of the CPU are collected: the allocated memory,allocated heap, and stack. These three values will be collected inintervals of 1 millisecond for a total of 5 seconds. This will generate5000 data points for each.

Next, the AI will start doing supervised machine learning on thesevalues, treating two as features and one as the predicted label.

Using a linear regression model, two features, let say the memory andheap, will learn to predict the stack label, then the model will collectnew values for the features and start predicting the heap label. Thesame machine-learning algorithm will be used, but with the labels beingthe other two features instead.

So, in total, we have three AI algorithms working simultaneously topredict three labels, memory, heap, and stack.

The three predicted values are truncated, using modular math, intospecific values depending on their allocated variables, as shown in thetable below.

TABLE.1 The features/labels transformation of the CPU metrics. FeaturesLabel Variable Mod Heap Memory Stack Note 7 Heap Stack Memory Tempo 6Memory Stack Heap Octave 12

The stack values will be allocated to the note variable and hence betruncated to mod(7), in other words, eight values from 0 to 7. Thememory values will transform into the tempo using mod(6), and finally,the heap variables will transform into the octave, using mod(12). Thesethree values will then pass on to the function table, as we to beexplained later.

1. The MathAI:

The MathAI shares the same supervised machine learning algorithm withthe MusicAI. However, for this case, the three predicted values of thememory, heap, and stack are truncated using mod(10). The operation isrepeated, and the values are concatenated to form one single number of aspecific length, specified by the programmer.

A single-digit of either [2, 3, 7, 8] is randomly chosen and then addedto the end of the concatenated number, whenever needed, to ensure thatthe number is not a perfect square. This is because no number, whensquared, will end with either of these four digits. The final number isthen square-rooted and passed on to the next element.

In summary, the AI outputs the following parameters:

-   -   a. The irrational seed. An infinite irrational number truncated        to a specific length.    -   b. The tempo, note, and octave parameters in the ranges of        (0-7), (0-8), and (0-13), respectively.

FIG. 2 is a schematic rendering of the workflow of the AI.

2. The Functions Table

The Functions Table is defined by a set of horizontal and verticalvariables that are mathematical functions proven to always produceperfect irrational numbers. The arguments of these functions are notfixed, determined by the random internal states, mainly the timestamp ofthe current time, as well as the tempo variable.

The tempo, note, and octave parameters coming out of the AI will be usedto determine which two cells on the vertical and horizontal axis will beutilized for the current run. The output of these cells (the irrationalmantissas) will then be truncated accordingly and used to compute thearithmetic mode by which the RBG will operate.

For our current model, we use the square root function on the horizontalaxis of the table and trigonometric ones on the vertical axis.

There are seven cells on the horizontal axis (FIG. 2 ), with theargument of the square roots being the product of the tempo value, thetimestamp (TS), and a non-square number (A) as follows: sqrt (TS x Tempox A). (This non-square number A is not the same as the N used togenerate the seed.)

The horizontal scale is made of 104 cells corresponding to 13 octaves,with each octave divided into eight notes. The octave parameter willfirst select one of the 13 octaves, and then the note parameter willselect which note of this specific octave will be used. Each notecorresponds to a trigonometric function having an argument made of thetime stamp divided by a specific frequency value: TS/fr.

The trigonometric functions, along with the frequencies of the notes ofthe 13 octaves, are listed in the table below.

TABLE 2 A list of the trigonometric functions used along with the musicfrequencies of each octave. Sin  432 × 100 450 468 252 270 288 306 324342 360 378 396 414 Cos  864 × 100 900 936 504 540 576 612 648 684 720756 792 828 Tan 1728 × 10 1800 1872 1008 1080 1152 1224 1296 1368 14401512 1584 1656 Ctan 3456 × 10 3600 3744 2016 2160 2304 2448 2592 27362880 3024 3168 3312 Sec 6912 × 10 7200 7488 4032 4320 4608 4896 51845472 5760 6048 6336 6624 Csc 13824 14400 14976 8064 8640 9216 9792 1036810944 11520 12096 12672 13248 Sin 27648 28800 29952 16128 17280 1843219584 20736 21888 23040 24192 25344 26496 Cos 55296 57600 59904 3225634560 36864 39168 41472 43776 46080 48384 50688 52992

Once the two irrational values of the horizontal and the vertical cellsare calculated, they will be truncated accordingly and then passed on,along with the seed, to the RBG.

3. The Random Bit Generator (RBG)

The RBG utilizes a specific mathematical function that takes the seedoutput of the AI as its initial argument and the two irrational numbersof the Functions Table as the arithmetic mod parameters. From there, ititerates on each calculated value to calculate new ones that are thenconcatenated to create a randomized sequence of bits.

The RBG general design is based on the cryptographically-secureBlum-Blum-Shub (BBS) generator2. But while the arithmetic mod in theoriginal BBS is computed from the product of a couple of prime numbers,in the CrownRNG case, we use the truncated irrational numbers comingfrom the Functions Table instead.

We can think of the RBG function as occupying the inner cells of theFunction table, taking its parameters from the X and Y axis, andoutputting a value based on these parameters and the seed.

The general concept of the BBS generator goes as follows:

-   -   1. Two primes p and q of specific bit-length are chosen such        that each is congruent to 3 modulo 4: p≡q≡3 mod(4). (In the        CrownRNG case, the two primes are replaced with two truncated        irrational numbers, I1 and I2, that satisfy the same mod(4)        requirement.)    -   2. The two prime numbers (irrational numbers in our case) are        multiplied to generate n, the arithmetical mode by which the        generator will perform its calculations.    -   3. A random integer s (the seed) is generated from another        physical true random number generator, having a length in the        interval of [1, n−1] (in the CrownRNG case, the seed is        generated by the AI.)    -   4. The seed will initiate the generation process through the        operation x₀=s²mod(n).    -   5. The function x_(i)=x² _(i-1)mod(n) is then used to iterate        over each previously calculated value, generating new values for        every iteration and outputting a string of numbers: x₁, x₂, x₃,        . . . , x_(k).    -   6. Next, the output values are converted into a string of binary        bits.    -   7. The bit-parity of each binary number is determined depending        on the type of parity, even or odd (0 or 1).    -   8. Finally, the parity digits are concatenated to form the        desired CSPRN, depending on the required bit-length of the key,        which also determines the level of security: Y=y₁y₂y₃ . . .        y_(k).

As mentioned above, the only modification the RBG introduces to theoriginal BBS is replacing the prime numbers with the irrational ones.The usage of prime numbers in the original BBS is a must if we want tohave the ability to reverse the direction of the generator, as in thecase when the BBS system is used as an encryption/decryption algorithm.However, as we do not want to reverse the operation in our system, thereis no problem with using numbers that are not prime. In fact, thisintroduces additional security to the system because when we compare thelimited amount of prime numbers having specific bit-length to theinfinite amount of potential irrational numbers of the same bit-lengths,the infinity factor introduces an extra advantage when it comes to thesecurity of the generator against cyber-attacks that try to predictthese values.

FIG. 5 shows a flowchart of a method of securing data, according toembodiments of the inventive subject matter.

At step 510, a computing device obtains a random selection of seeds. Theseed can be selected in several ways.

In embodiments, the seed is selected randomly from among numbers thatare neither prime numbers nor quasi-prime numbers.

In embodiments, the seed is randomly selected from among a plurality ofnumbers that are over a thousand digits long. In other embodiments, theseed is randomly selected from among a plurality of numbers that areover ten thousand digits long.

At step 520, the computing device uses the seeds to generate irrationalnumbers. The generation of irrational numbers is discussed in furtherdetail below.

FIG. 6 illustrates the processes associated with encrypting a set ofdata according to embodiments of the inventive subject matter. Steps610-660 cover the process of encrypting a message or data.

At step 610, the sending computing device selects a function to be usedto obtain an irrational number. The function can be a mathematicalfunction or algorithm as discussed further herein. The function can beselected according to a pre-determined order or schedule. Alternatively,it can be randomly selected or user-selected. The computing deviceobtains the selected function from the stored functions in a functionsdatabase.

At some point prior to step 620, the computing device also obtains aplurality of seeds, as discussed above.

At step 620, the computing device solves the function using each of theselected seeds to obtain a corresponding irrational number. Irrationalnumbers have an infinite or near-infinite amount of decimal places.Thus, the function is a function whose output is an irrational number.By using an irrational, the systems and methods of the inventive subjectmatter have the flexibility to obtain many encryption keys from the samefunction without repeating some or all of the encryption keys. Becauseirrational numbers do not have a pattern, the systems and methods of theinventive subject matter can ensure true randomness in the generation ofcryptography keys. For example, the function can be to take the squareroot of a non-perfect square number. This results in an irrationalnumber. In an illustrative example, the function to be solved can be thesquare root of 20.

In embodiments, solving the function comprises taking an inverse of eachof the selected seeds.

In embodiments, the irrational number is calculated by calculating theroot of the seed.

In embodiments, the root can be a square root or a cube root. In otherembodiments, the root can be a fractional root.

In embodiments, the irrational number can be a root of a number thatcomprises the seed and that ends in 2, 3, 7 or 8.

In embodiments, the same function is not applied to all of the obtainedseeds. In these embodiments, the computing device selects a firstfunction and applies it to a first subset of the obtained seeds. Thecomputing device then selects a second function and applies it to asecond subset of the obtained seeds. The total group of selected seedscan be subdivided into additional subsets and have additional functionsapplied to them.

At step 630, the computing device selects a starting point and a lengthwithin the mantissa of each irrational number calculated for each seed.The starting point designates a start digit in the mantissa. The lengthdesignates the number of digits following the start digit. The startdigit and length are preferably integer values such that they identify aprecise digit location and precise length.

At step 640, the computing device applies the starting point and lengthto the decimals of the mantissa to result in a shortened key or one-timepad, which is a portion of the mantissa. Thus, the one-time pad is a keythat starts at the start digit and contains the digits following thestart digit according to the length.

In embodiments, the one-time pad can be at least 10,000 digits long. Inother embodiments, the one-time pad comprises at least as many digits asdata positions in the data. In still other embodiments, the binaryrepresentation of the one-time pad comprises at least as many digits asthe binary representation of the data to be encrypted. After step 640,the process continues to step 530 of FIG. 5 .

The techniques used to generate and use the encryption/decryption keysusing a mathematical function are described in greater detail in theinventor's own pending U.S. patent application U.S. Ser. No. 17/018,582filed Sep. 11, 2020, entitled “Method of Storing and Distributing LargeKeys”, which is incorporated herein by reference in its entirety.

At step 530, the computing device uses the generated portion of themantissas of each of the irrational numbers as a one-time pad to encryptindividual ones of multiple pieces or sets of data. The encrypted datacan then be stored by the computing device locally or at a remotedatabase.

At step 540, the computing device updates its records of used seeds anddiscards those seeds. Discarding the seeds can involve deleting theseeds from the database that stores the seeds In a variation of theseembodiments, the computing device can discard the starting points andlengths used such that the seeds themselves can be reused but thestarting points and lengths are not such that the actual one-time padsused for encryption cannot be recreated by the computing device.

In embodiments, the first portion (which can be or can include the seed)can be distributed via a graphical code. This graphical code could be aQR code. In a variation of these embodiments, the QR code can containadditional codes that help to obfuscate the public key.

To decrypt the encrypted data at a future time, the computing device (oranother computing device that is the recipient of the encrypted data)can apply the same seeds to the function to generate the mantissa andone-time pad as discussed above, to generate an identical key that canbe used for decryption.

In situations where a receiving computing device is decrypting the data,the sending computing device can send the seed and an indicator of afunction. The receiving computing device would already have thefunctions (or pointers to these functions) stored as part of an initialshared secret established prior to the data transmission. The receivingcomputing device would also receive or otherwise obtain the startingpoints and lengths for each of the one-time pads it needs. The seed(s)can be transmitted as part of a graphical code as discussed above.

A benefit of this approach is that for each potential recipient that maybe authorized to access to some of, but not all of, the individualencrypted data sets, the system can provide access to only the data setsthat particular recipient is authorized to access. To do so, thecomputing device can send the necessary decryption information for onlythe authorized data sets. This way, the recipient computer device canonly decrypt and access the data for which it has the decryption tools.

It should be apparent to those skilled in the art that many moremodifications besides those already described are possible withoutdeparting from the inventive concepts herein. The inventive subjectmatter, therefore, is not to be restricted except in the spirit of theappended claims. Moreover, in interpreting both the specification andthe claims, all terms should be interpreted in the broadest possiblemanner consistent with the context. In particular, the terms “comprises”and “comprising” should be interpreted as referring to elements,components, or steps in a non-exclusive manner, indicating that thereferenced elements, components, or steps may be present, or utilized,or combined with other elements, components, or steps that are notexpressly referenced. Where the specification claims refers to at leastone of something selected from the group consisting of A, B, C . . . andN, the text should be interpreted as requiring only one element from thegroup, not A plus N, or B plus N, etc.

What is claimed is:
 1. A method of encrypting and decrypting multiplepieces of data, comprising: using a computing device to provide a randomselection of seeds; applying at least one function against the randomselection of seeds to produce corresponding irrational numbers; usingportions of the irrational numbers as one-time pads; applying theone-time pads to encrypt or decrypt individual ones of the multiplepieces of data, respectively; and utilizing a system that avoids reusingpreviously utilized seeds.
 2. The method of claim 1, wherein individualones of the random selection of seeds are neither primes norquasi-primes.
 3. The method of claim 1, wherein the step of using acomputing device to provide a random selection of seeds comprisesrandomly selecting the random selection of seeds from a pool of previousrandomly selected seeds.
 4. The method of claim 1, wherein at least someof the random selection of seeds comprise over a thousand digits.
 5. Themethod of claim 1, wherein at least some of the random selection ofseeds comprise over ten thousand digits.
 6. The method of claim 1,wherein the at least one function comprises taking an inverse ofindividual ones of the random selection of seeds.
 7. The method of claim1, wherein the at least one function comprises taking a root ofindividual ones of the random selection of seeds.
 8. The method of claim7, wherein the root is a square root or cube root.
 9. The method ofclaim 7 wherein the root is a fractional root.
 10. The method of claim1, further comprises applying a first function against a first subset ofthe random selection of seeds, a second function against a second subsetof the random selection of seeds, and wherein the first function isdifferent from the second function, and the first subset is differentfrom the second subset.
 11. The method of claim 1, wherein at least someof the one-time pads comprise at least 10,0000 digits.
 12. The method ofclaim 1, wherein at least some of the one-time pads comprise at least asmany digits as data positions in the corresponding pieces of data beingencrypted.
 13. The method of claim 1, wherein binary representations ofat least some of the one-time pads comprise at least as many digits asdigits in binary representations of the corresponding pieces of databeing encrypted.
 14. The method of claim 1, further comprises makingavailable to a recipient for decryption of an encrypted message,multiple ones of the random selection of seeds.
 15. The method of claim1, wherein the system avoids reusing previously utilized seeds bystoring representations of previously utilized seeds, and rejecting foruse individual ones of the random selection of seeds that matched thepreviously utilized seeds.
 16. The method of claim 1, wherein the systemavoids reusing previously utilized seeds by never reusing for encryptionany of the previously utilized seeds.